Crystals are uber important items that were introduced in Crash Bandicoot 2: Not N-Tranced. They apparently have massive power. And are purple.
When Uncle Cortie fell to his not-death in Crash Bandicoot 2: Cortex Has Plans That Are To Be Stricken From The Record, he found a crystal. It was one of many. He then took it, and decided to get his immortal enemy to get some more for him. Of course, Crashie succeeds, and refuses to give them to Cory. What a dick. So, Corz is defeated. And tries to get more from different time era places in Crashing To Different Time Periods, in the last time crystal collecting made sense. There were only supposed to be a few crystals total. So, instead, they illogically need to be collected in Crunch Bandicoot, Crash At Your Fingertips 1, and Crash At Your Fingertips 2. They were also collectables in Bonus Rounds in Crash Gets His Driver's License and Crash Loses His Driver's License. And Eurocom Tries Their Hand At Bandicoots. No logic, I swear! There were supposed to only be 25 total! We're up to, what, 120 by now? Especially with the weird count Tranny N'ced had. Oh, and I think crystals played some role in Twash Crinsanity, but that game sucked. If memory serves, they were little more than replacements for Neoie's penis, so his bandicoot companion had something to tug. It was weird.